Puzzles 101 A Puzzle masters Challenge

This latest collection of puzzles from the internationally acclaimed puzzlemaster Nob Yoshigahara covers a wide variety of puzzles from physical to visual, conceptual to mathematical. Solutions are provided in a separate section, which will help novices get on the right track, and will give seasoned aficionados a chance to check their work

9 `

—— Puzzles 101 2

Puzzles 101 $8,

A Puzzlemaster’s Challenge # |

Nobuyuki Yoshigahara

Translated by Richard Weyhrauch and Yasuko Weyhrauch

A K Peters Natick, Massachusetts

Yoshigahara, Nobuyuki, 1936-

{Chocho nanmon suri pazuru English}

Puzzles 101: a puzziemaster’s challenge / Nobuyuki Yoshigahara ; translated by Richard Weyhbrach and Yasuko Weyhbrach

Preface ix

> Two Different Lengths 1, 67

Crossing the River 2, 67 Making a Die 3, 68 What Comes Next? 3, 68 Diamond Puzzle 4, 69 The Water Puzzle 5, 69 The Opposite of Puzzle 6 6, 70 Three Times More 6, 70 Triangular Arithmetic 7, 71 Triangular Solitaire 8, 71

The Same Area 9, 72

Lose Those Squares 10, 73

Two Choice Question 10, 73

Triangulation 11, 74

Rock, Paper, Scissors 11, 74

Four Solutions of Four Pieces! 12, 75

Four Solutions of Four Pieces Il 12, 75

Pandigital (Komachi) Fraction! 18, 80

Pandigital (Komachi) Fraction Il 18, 80

Cut and Rearrange a Cross 32, 92

The Curious Door Sign 33, 93

Triangle Struggle 33, 93

Place the Coins 34, 94

Cut and Paste! 34, 94

Cut and Paste Il 35,95

Trick Name Card! 35, 95

Trick Name Card Il 36, 95

Uniform Division 36, 96

Three Contacting Matchsticks 37, 97

Find the Rule 37, 98

Typewriter 38, 98

Seven Straight Lines 38, 98

Four and a Half Tatami Mats 39, 99

Five Consecutive Numbers 40, 100

Chocolate 40, 100

A Go Stone Puzzle 41, 100

Coins in Two Dimensions 41, 101

Puzzles 101

Time Calculation Using Pandigitals (Komachi) 51, 109

Time Calculation Using Pandigitals PlusO (Komachi) 51, 109

How Many Loops? 52, 110

Up and Down Maze_ 53, 111

Jumping Go Stones 54, 112

Moving Matchsticks 55, 112

One Place the Same_ 56, 113

The Same Product 57, 113

Height and Weight 60, 116

Tail Becomes Head 61, 117

Is the Opposite Also True? 61, 117

Be ET

The famous German poet Hans Magnus Enzensberger concluded his essay on the isolation of mathematics

in our society with an appeal for action: “The effort

in question is nothing short of the achievement

of mathematical literacy which will furnish our all

to sluggish brains with a kind of athletic work-out and yield to us a variety of pleasure to which we are entirely unaccustomed.” Those of us in the international puzzler’s league have anticipated his advice and pursued our belief in the stimulating and entertaining quality of advanced puzzles Puzzle creators and solvers are a close-knit community and our creations travel by word of mouth like the great poems, fairy tales, and sagas of the world A gradual expansion into the wider community is changing the communication and the influence of our art Judging

by the growing popularity of books dealing with advanced puzzles, we are successful in spreading the word, and it has always made me proud and happy

to see puzzles that | created appearing in such books Suddenly, | began to worry: If |ever wanted to publish

a book of my puzzles, would people not look at me like a thief? So | decided to start my own collection sooner rather than later, and | present, in this small volume, many puzzles that | invented and a number

of puzzles created by my friends that | particularly like | include those puzzles with their permission and mention their name as a small tribute If you, dear Reader, find a puzzle without a name that you believe was made by someone else, please notify

me or the publisher so that credit can be given where credit belongs

My selection comes from a huge pile of puzzles and my choices were driven by my own taste and

Puzzles 101

the desire to balance advanced and simple, but entertaining, puzzles to keep the reader interested and motivated | don't believe that anybody could solve all these puzzles in one year; | certainly could not do it if | did not know the solutions already But here is a condition that you must obey: Do not use a computer! Remember what Enzensberger said: “

an exercise to give our all too sluggish brains [not our computer] a work-out.”

| used to be a maniac about solving hard puzzles and | had a lot of fun (and some frustration) doing

it Now, | have become a taskmaster who creates puzzles for others to enjoy and agonize over Let me tell you that the reward of such agonizing is the great joy of “Eureka!” You may get addicted, but this kind

of addiction will only help your brain, not destroy it Let me thank all who have allowed me to use their ideas, and let the joy of our readers be a reward for all of us who care about and puzzle over hard problems with elegant solutions

Puzzles 101

points are allowed to be in the same location

(Puzzle by Dick Hess)

Puzzles 101

Four boats A-D are on the left bank of a river To cross

the river to the right bank, Boat A takes 2 minutes;

Boat B takes 4 minutes; Boat C takes 8 minutes; and

Boat D takes 16 minutes

The four boats need to go to the right bank,

but there is only one boatman One boat can pull

another boat, but it will take the same amount of time

as the slower of the two boats to cross the river

lf the boatman uses one boat to pull another

boat to the right bank and returns to the left bank

in one boat, how many minutes will it take for him

to move all the boats to the right bank? Find the

shortest time (ignore the time he spends changing

and connecting boats)

Puzzles 101

?

Fold a square into a 3 x 3 grid

Cut out the square in the

middie and cut one section ~ —

as shown here You now have

eight small squares Can you

fold this paper and make it into

a cube? Since a cube only L L

has six surfaces, you need to | |

overlap some squares

What comes after 662

2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46, 50, 52, 54,

56, 60, 62, 64, 66, ?

Puzzles 101

°

A square is missing one-quarter of its area; we want

to turn it into the diamond shape in Figure 1 by cutting it into two pieces and rearranging them

^Z

Figure ]

In Figure 2, we cut the square into four pieces and rearranged them Can you find a way to cut and rearrange fewer pieces and make a diamond?

MALY

Figure 2

Eight coins are arranged to look like the letter H By sliding one coin around at a time, we want to arrange the eight coins to look like the letter O However, there is a strict rule: A moving coin needs to stop in a

position where it touches at least two coins

Hi)

Figure 1 Figure 2

In Figure 1, the moving coin ends up touching two coins, but in the Figure 2, the moving coin ends up touching only one coin, so it is prohibited

° 8 Figure 3

In Figure 3, a moving coin is indeed touching two coins, but this coin will not stop right there—it will slide on; therefore, such a move is also prohibited

Please get eight real coins and play with them

lf you form the letter O in five moves, | will be really

impressed

By the way, | call this puzzle “The Water Puzzle” because it changes H to O (H,O)

Puzzles 101

°

§008

Continue from Puzzle 6 This time, each coin needs to be

moved around so that the eight coins arranged as the

letter O change into the letter H The minimum number

of moves is seven—this puzzle is much more difficult

| divided a square into three parts The lines labeled

with one circle are the same length, and the length

of the line with two circles is twice as long as the lines

with one circle

Get some paper, cut three squares, and then

cut each of them into three pieces as shown here

Now, using the nine pieces cut from the squares,

create a square whose area is three times that of the

original square

This puzzle will be less difficult if you actually

make the pieces

?

““““Triangulor Arithmetic Puzzle 2

Arrange the numbers 1 ton (where nis a “triangular” number) to form an equilateral triangle in such a way that the difference between two neighboring numbers is right below them Figure 1 shows some samples:

⁄)

Puzzle 10 Triangular Solitaire

Connect ten circles in the form of an equilateral

triangle as shown Put one coin on each circle and

follow these steps:

1 Remove one of the coins

2 Pick another coin If there is a coin on a circle

adjacent to the coin you chose and the circle

beyond that coin is empty, then you can jump

over that coin and take it away

3 Repeat Step 2 You are done when there is

only one coin left

Advanced: Try to solve this in as few steps as

possible Jumping continuously is counted as one

step

Puzzles 101

eng "2 Lose Those

Squares

Arrange 20 coins as in the picture We can create

21 squares by connecting the centers of four of the

coins (an example is shown) Now remove as few

coins as possible until no square can be made

Puzzle 13 two choice QUESTOR —

There are ten questions for which you can choose

O or X as the answer Each right answer is worth ten

points The results for Students A, B, and C are as

shown in the table But the teacher has forgotten to

write down the total score for Student D, and he also

has lost the correct answer for each question From

the table, find out D's score

Puzzles 101

ie

Triangulation Puzzle 14

2”

A triangle is divided into four parts by two straight lines

as shown The area ratio of the three parts is 3:7:7

What is the size of the fourth area?

ẹ

A boy and a girl played Rock, Paper, Scissors ten

times The boy used three rocks, six scissors, and one

paper The girl used two rocks, four scissors, and four papers

There was never a tie, and the order in which the boy and girl used rocks, papers, and scissors is unknown Who has won by how many wins?

(Puzzle by Yoshinao Katagiri)

“2

Puzzle 16 Four Solutions of Four Pieces 1"

G

Cut this shape into four

identical pieces Don't

stop after you find one

solution’ ve found four

Use the same rule as in

Puzzle 16; try to find four

Cut the shape on the left into two parts and

reconnect them to make a square

Simultaneous

Equations

CHDXHLui LIxLI=LIH

Fillin each of the squares with one each of nine digits

1 to 9 so that both equations are correct

Puzzle 19

Puzzle 20 Even Number

Ten coins are arranged on a 4 x 4 board, in the

picture As shown here, there are eight (horizontal,

vertical, and diagonal) sequences where an even

number of coins is lined up Rearrange the ten coins

so that you have the largest number of sequences

with an even number of coins Try to find an

arrangement where you have the least number of

sequences as well

cả

Age Guessing Puzzle 2)

Father: | have just realized that, if | switch the number

in the ones digit and in the tens digit of my age, | get

your age

Son: Tomorrow you will be exactly twice as old as I

How old are they as of today? Don’t be too quick to answer

+

Divide by Four Puzzle 22

This shape is half of a regular hexagon Divide it into

four identical shapes; you can flip over shapes I’ve

found two solutions

LAUGHING has it, but not CRYING

HIJACK has it, but not TERRORISM

FIRST has it, but not SECOND

AFGHANISTAN has it, but not TAJIKISTAN

CALMNESS has it, but not NOISE

DEFINE has it, but not DECIDE

What is it?

?

Five squares can be connected in 12 different ways,

as shown in Figure 1 We consider two shapes to be

the same if they become identical by flipping one of

different solutions can you find? You are allowed to

flip over the shapes

Figure 2

Fill out the squares in the equation using the numbers

1 to 9 once and only once Two boxes together is a

[IxFI T ñxĩI TTIxHT~ !

Fill out the squares in the equation using the numbers

1 to 9 exactly once

So far, | know of two solutions

Fill an 8 x 12 grid using 32 1 x 3 pieces so that a

“cross” is not formed A “cross” is formed when two

lines intersect at a four-way junction

Note: Japanese tatami mats are arranged as

in Examples | and Il such that no line crosses the

room Tatami mats would never be arranged as

in Example Ill Don Knuth created this puzzle when

he visited Japan and had a conversation about tatami mats with

me Since the I I Il given condition is

severe, a solution | can be_ found

easily If there are no restrictions, there are 51,493 different solutions Thanks to this restriction, there are

only two solutions

Puzzles 101

pee Puzzle 30

Arrange the numbers 1-15 so that the sum of two

neighboring numbers is always a square number

“Square Num

Hint: You can find a solution using pencil and

paper The same square number will be used more

A white wooden piece and a black wooden piece

are interlocked as shown

Can you guess how they might come apart easily? There is no hollow space inside The bottom

view is just a black rectangle abutting a white

rectangle

Two diameter 1 coins fit into a diameter 2 circle;

seven diameter 1 coins fit into a diameter 3 circle

How many diameter | coins will fit into a diameter 4

circle?

Puzzles 101

?

Pick two numbers from 2-9 Create a number using

the numerals for these two numbers in such a way

that it can be divided by either of the two numbers

For example, 48 or 488 can be created using 4 and

8, and each of them can be divided by both 4 and

8 If you use 2 and 4, the smallest such number is 24

If you use 3 and 5, the smallest such number is 3555

Find two numbers so that the least such number is

the largest of all the combinations

This puzzle was named LYM (Least Yoshigahara Multiple) by Technology Review from M.1.T

"BUG House Puzzle 35

Place these nine bug-shaped pieces into the

triangular honeycomb shape You can rotate

them, but you cannot flip them over Notice that

two pieces have already been flipped over: these

cannot be flipped back

Fillin the space by pencil Itisnotsohard ¢ |

Puzzles 101

Black dots are arranged as a 4 x 4 grid as pictured

Connect the center of each dot in one stroke to form a

loop One solution is shown here; find another solution

Equal Distance Puzzle 38

Consider the four vertices of this square Each vertex

is an equal distance from the two vertices to which

it is connected

Place nine points on a flat surface so that any

point is an equal distance from three other points

Find one example

2

Puzzle 39-n—

3:59:33

A palindrome is an expression which reads the same

both forward and backward Look at this clock It

shows exactly the same time by reading from left to

right and from right to left(ignoring”:”) On a 24 hour

clock there are 660 times each day when we have

such a time Now find the following times:

1 The two palindrome times that are the closest

2 The two palindrome times that are the farthest

apart with no palindrome times between them

3 The two palindrome times that are the farthest

apart if other palindrome times are allowed

between them